Summary

Visualization, understanding and interpreting real data may be challenging because of noise in the data, data complexity, multiple variables, hidden relations between variables and large variation. This NISER activity demonstrates how to use free Internet-based IT-tools and resources to solve problems that arise in the areas of biological, chemical, medical and social research.

Motivation/Problem

Mercury contamination of edible freshwater fish poses a direct threat to human health. Largemouth bass is a fresh water fish that was studied in 53 different Florida lakes to examine the factors that influence the level of mercury contamination. Water samples were collected from the surface of the middle of each lake in August 1990 and then again in March 1991. The pH level, the amount of chlorophyll, calcium, and alkalinity were measured in each sample. Also, samples of fish were taken from each lake with sample sizes ranging from 4 to 44 fish. The age of each fish and mercury concentration in the muscle tissue was measured. Since fish absorb mercury over time, older fish will tend to have higher concentrations. Here is a detailed discussion of why mercury accumilates in muscle tissues and why is it toxic in larger amounts.

Largemouth bass were studied in 53 different Florida lakes to examine the factors that influence the level of mercury contamination. Water samples were collected from the surface of the middle of each lake in August 1990 and then again in March 1991. The pH level, the amount of chlorophyll, calcium, and alkalinity were measured in each sample. The average of the August and March values were used in the analysis. Next, a sample of fish was taken from each lake with sample sizes ranging from 4 to 44 fish. The age of each fish and mercury concentration in the muscle tissue was measured.

Challenge

Common risks with eating fish.

To make a fair comparison of the fish in different lakes using a regression estimate of the expected mercury concentration in a three-year-old fish as the standardized value for each lake. Determine the age of the individual fish in some lakes and correlate this with the average mercury concentration of the sampled fish.

Florida has set a standard of 1/2 part per million as the unsafe level of mercury concentration in edible foods. 45.3% of the lakes exceed this level. The smallest level of mercury concentration that the measuring instrument can detect is 40 parts per billion. Any level below that was set to 40 parts per billion. This, of course, "flattens out" the slope of the relationship at the low end as well as affecting the standardized values. These observations are usually on young fish.

Logarithmic transformations on some of the variables may provide insights into the relationships among the other variables in the study. For instance, alkalinity level may be associated with mercury concentration, and may help account for the higher levels of mercury.

Methods & Approaches

We now discuss varieties of scientific methods, models, tools and strategies for data modeling, understanding, inference and visualization of the data in this specific driving biological problem, as well as, discuss checking and affirming underlying model or technique assumptions.

Alkalinity represents the ability of a solution to neutralize acids to the equivalence point of carbonate or bicarbonate. Alkalinity is closely related to a solution's acid neutralizing capacity. However, the acid neutralizing capacity refers to the combination of the solution and solids present and the contribution of solids can dominate the acid neutralizing capacity.

Mercury uptake by plants

Mercury uptake by plants is low (Jenkins, 1981; Paasivirta, 1991), however plants may be used for monitoring mercury contaminations.

Trees uptake mercury through the xylem, from soil via the root system or from direct deposition via foliage and bark.

The Biology of mercury uptake:

In fish, mercury appears primarily as methylmercury and that's the most common form of mercury transfered through the food chain.

Methylmercury is produced initially by microbial activity, as it is insoluble in water, and forms colloids with humus, which in turn transfer mercury from soils to water.

Dissolved organic carbon complexes transport mercury.

As pH decreases, partitioning of mercury is shifted from sediment to water.

The major pathways for mercury removal from solution is chemical binding with reduced sulphur, which has a high affinity for mercury.

Increased concentrations of some metals, e.g., iron and manganese, affect the non-biological methylation of mercury. Acid volatile sulfides like iron and manganese sulfides are a reactive pool of solid phase sulfides are available to bind with metals, such as mercury (Di Toro et al., 1990), which makes mercury is less available for uptake by fish.

Ethotoxicology

Ethotoxicology is the study of the behavioral consequences of exposure to toxic chemicals. Toxic chemicals, like heavy metals and estrogen mimicking compounds, may influence behavior. For instance, there are documented changes in how some animals respond to novel situations, vocalize, and expose themselves to the risk of predation as a function of chemical exposure. Thus, by quantifying time allocation using an event recorder (like JWatcher), and using various statistical analyses to analyze these data, it is often possible to have a behavioral indicator of chemical exposure. And, by quantifying such behaviors in a variety of species, and then using phylogenetic software (like Mesquite), it is possible to study the evolution of such behavioral effects. We are in the process of developing new applets and learning materials demonstrating the effects of toxic exposure to such compounds on animal behavior.

Mercury biomagnifies as it moves up trophic levels in the food chain. Biomagnification by plankton from water may be as high as 100,000 times. Food web enrichment is apparent in plankton and aquatic insects, insect-eating fish, piscivorous fish, and fish-eating birds (Paasivirta, 1991).

Mathematics

We can easily compute the histogram of the average (per lake) mercury measurements and fit in Normal, Exponential or other distribution models to the histogram of the average mercury measurement using SOCR Charts and SOCR Modeler (see examples here). The left image below shows the fit of a Normal(μ = 10.54,σ2 = 45.64) distribution model and the right image shows the (offset by 0.8) Exponential(λ = 10.54) model fit to the mercury histogram. The parameters in both cases are automatically calculated from the data using maximum likelihood estimation.

We can also demonstrate the effect of using a wavelet decomposition of the column data (avg_mercury). The image below demonstrates the wavelet representation of this column vector data using Daubechies' 2 wavelet basis, where only the largest 10% of the wavelet coefficients were used to reconstruct/synthesize the (compressed) wavelet representation of the data. More information about wavelets and wavelets-based activities may be found here. You can use the SOCR Modeler to fit is any of a number of wavelet models to data and observe the effect of wavelet shrinkage on the corresponding wavelet model fit.

Statistics

Are there associations in these data between Alkalinity, pH, Calcium and Chlorophyll? Using SOCR Analyses construct regression plots illustrating the relations between Calcium, Chlorophyll and Avg_Mercury, as shown on the image below.

Generate some exploratory data analyses (EDA plots). For instance, the figure below demonstrates how you can use SOCR Charts to obtain the scatter plot of Alkalinity vs. pH. What are some inferences about the bivariate relations between these variables?

What is the distribution of the average amount of mercury in the entire sample? We can use SOCR Charts to construct the histogram of the avg_mercury column data. To learn how to use SOCR Charts see these Charts Activities. Notice the effect the bin-size parameter has on the shape of the data histogram (you can smoothly vary this parameter). Although, there are many choices for determining the bin-size parameter, in general, the optimal choice of the histogram bin-size parameter may be determined by , where the interquartile range IQR = Q3 − Q1, and Q3 and Q1 are the third and firstquartiles for the sample data, respectively.

Is there evidence of statistical differences between the two groups (according to the age_data variable) in either Alkalinity or pH?

There does not seem to be a statistically significant difference in the pH levels between the two groups separated by the age_data varaible. A non-parametric Wilcoxon Rank Sum test did not produce significantly small p-value (see the image below showing the result of the calculations using SOCR Analyses.

Similarly, there does not seem to be a statistically significant difference in the Alkalinity levels between the two groups separated by the age_data variable. The same non-parametric Wilcoxon Rank Sum test did not produce significantly small p-value (see the image below showing the result of the calculations using SOCR Analyses.